1. Field of the Invention
The present invention relates to a measuring method and apparatus and more particularly, the present invention is suitable for use in optical heterodyne interference arrangements, for example, a very small displacement measuring apparatus, an alignment apparatus, a brazing registration evaluation apparatus, a length measuring instrument, or an apparatus which measures a very small displacement of an object by using a diffraction means, such as a diffraction grating.
2. Description of the Related Art
Hitherto, a heterodyne interference method capable of detecting information on the phase of light which is in a linear relationship with displacement by phase detection has been widely used for the high-precision measurement of a very small displacement. In the heterodyne interference method, measurements are performed in such a way that interference fringes which change in relation to time and are formed by two light beams whose frequencies are slightly different from each other are photoelectrically detected, and the phase of the interference fringes is converted into the phase of an electrical signal.
FIG. 1 shows a conventional embodiment, which is a very small displacement measuring apparatus which uses a Zeeman laser 301 for a light source and utilizes linearly polarized light beams 302 and 303 intersecting at right angles with each other, frequencies thereof being slightly different from each other, and which constitutes an interferometer. The light 302 is P polarized light having a frequency f.sub.1, the electrical vector of which is light within the diagram. The light 303 is S polarized light having a frequency f.sub.2, the electrical vector of which is light perpendicular to the diagram. Complex amplitude displays E.sub.1 and E.sub.2 of respective lights 302 and 303 emitted from the Zeeman laser 301 can be expressed as follows when their respective initial phases are denoted as .phi..sub.1 and .phi..sub.2 : EQU E.sub.1 =A.sub.0 exp {i (w.sub.1 t+.phi..sub.1)} (1) EQU E.sub.2 =B.sub.0 exp {i (w.sub.2 t+.phi..sub.1)} (2)
where A.sub.0 and B.sub.0 are amplitudes, w.sub.1 and w.sub.2 are angular frequencies, w.sub.1 =2.pi. f.sub.1 and w.sub.2 =2.pi. f.sub.2. Lights 302 and 303 are each amplitude-divided by a beam splitter 304. Either one of light 302 or 303 becomes reference light 306 or 307, and either one of light 302 or 303 becomes signal light 315 or 316 which enter an interferometer.
At this time, the polarization directions of the reference lights 306 and 307 are aligned by a polarization plate 305 (a polarizer for extracting polarization components which are inclined by 45.degree. in their respective polarization directions) and are detected by a photoelectric detector 317. Complex amplitude displays E.sub.1R (the complex amplitude of light 307) and E.sub.2R (the complex amplitude of reference light 306) of the reference light beams 307 and 306 at this time are as shown below if L.sub.S and L.sub.0 denote respectively an optical path length from the light source 301 to the beam splitter 304 and an optical path length from the beam splitter 304 to the photoelectric detector 317, as shown in FIG. 1, and A.sub.1 and B.sub.1 denote the respective amplitudes of these displays E.sub.1R and E.sub.2R : EQU E.sub.1R =A.sub.1 exp [i {(w.sub.1 t+.phi..sub.1 -k.sub.1 (L.sub.S +L.sub.0)}] (3) EQU E.sub.2R =B.sub.1 exp [i {(w.sub.2 t+.phi..sub.2 -k.sub.2 (L.sub.S +L.sub.0)}] (4)
where k.sub.1 and k.sub.2 represent the number of waves. If c denotes a light velocity, the following relations are satisfied: ##EQU1## The polarization direction of the reference light beams 306 and 307 are aligned by the polarization plate 305 so that light beams 306 and 307 interfere with each other. When this interference light is photoelectrically detected by the photoelectric detector 317, a detection signal I.sub.R is: EQU I.sub.R =A.sup.2.sub.1 +B.sup.2.sub.1 +2A.sub.1 B.sub.1 COS {(w.sub.1 -w.sub.2) t+(.phi..sub.1 -.phi..sub.2)+(k.sub.2 -k.sub.1) (L.sub.S +L.sub.0)} (5)
This detection signal is a beat signal having an angular frequency of w.sub.1 -w.sub.2, i.e., a frequency of f.sub.1 -f.sub.2, and a phase of .phi..sub.R =(.phi..sub.1 -.phi..sub.2)+(k.sub.2 -k.sub.1) (L.sub.S +L.sub.0). In contrast, light which is transmitted through the beam splitter 304 enters a polarization beam splitter 308. Light beam 315 of S polarization is reflected thereby, is reflected by a mirror 310, and travels again toward the polarization beam splitter 308. At this time, the polarization direction is rotated by .pi./2 as a result of the light beam 315 passing two times through a .lambda./4 plate 309 disposed in the optical path. Because the light has become light of P polarization, it is transmitted through the beam splitter 308. Light beam 316 of P polarization is transmitted through the polarization beam splitter 308 and is reflected by an object 312 to be measured. The light beam 316 travels again toward the polarization beam splitter 308. In the same manner as described above, the polarization direction is rotated by .pi./2 as a result of light beam 316 passing two times through a .lambda./4 plate 311 disposed in this optical path. Because the light beam has become light of S polarization, it is reflected by the polarization beam splitter 308. Thereafter, the polarization directions of signal light beam 316 of S polarization and signal light beam 315 of P (5) and (8) is measured by using a lock-in amplifier 319 as a synchronization wave detector.
The difference .DELTA..phi. between the phases of the beat signals shown in equations (5) and (8) is determined as shown in the following equation: EQU .DELTA..phi.=(k.sub.2 -k.sub.1) (L.sub.0 -L.sub.1)-2k.sub.1 .DELTA.L.
By rearranging this, it follows that: ##EQU2## If .DELTA..phi..sub.0 when .DELTA.L=0 is measured beforehand, L.sub.0 -L.sub.1=.DELTA..phi..sub.0 /(k.sub.2 -k.sub.1). Since k.sub.1 and k.sub.2 are known, L.sub.0 -L.sub.1 can be determined.
Thereafter, if the difference .DELTA..phi. between the phases of the two beat signals shown in equations (5) and (8) is measured, a displacement .DELTA.L of an object to be measured can be determined on the basis of equation (9).
However, the resolution of such a heterodyne interference measurement depends upon the resolution of a phase measuring apparatus which measures the phase difference between two beat signals. To increase the measurement resolution, the resolution of a phase measuring apparatus must be increased. However, there is a technical limitation regarding this.
Hitherto, a so-called optical encoder which measures a movement amount or a rotation amount of an object by using an optical scale has been used in the field of mechanical control. A conventional optical encoder has been disclosed in, for example, Japanese Patent Laid-Open No. 58-191907. In this optical encoder, coherent light from a light source is made to enter a diffraction grating which is a reference scale through a mirror or the like. .+-.N-th-order diffracted light emitted from this diffraction grating is reflected by a corner cube to its original direction and is also made to enter the diffraction grating. Then, two diffracted light beams of .+-.N-th order are diffracted in the same direction to interfere with each other. The intensity of the resulting interference light is detected by an optical sensor.
Since such an apparatus is small and can achieve a high resolution, it has been used for various purposes and for a variety of applications.
As machining and control have become more precise and fine, it has been required that such a measuring apparatus have a higher resolution than ever before.